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问题 2936. -- 「一本通 6.6 练习 5」Combination

2936: 「一本通 6.6 练习 5」Combination

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题目描述

<div class="ui bottom attached segment font-content"><div style="position: relative; overflow: hidden; "><p><strong>原题来自：<a href="https://www.lydsy.com/JudgeOnline/problem.php?id=2982">BZOJ 2982</a></strong></p>
<p>LMZ 有 <span class="katex"><span class="katex-mathml">nn</span><span class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em; vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span></span></span></span> 个不同的基友，他每天晚上要选 <span class="katex"><span class="katex-mathml">mm</span><span class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em; vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">m</span></span></span></span> 个进行 [河蟹]，而且要求每天晚上的选择都不一样。那么 LMZ 能够持续多少个这样的夜晚呢？当然，LMZ 的一年有 <span class="katex"><span class="katex-mathml">1000710007</span><span class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em; vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mord mathrm">7</span></span></span></span> 天，所以他想知道答案 <span class="mjx-chtml"><span class="mjx-math"><span class="mjx-mrow"><span class="mjx-mo" style="padding-left:0.278em; padding-right:0.278em;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top:0.372em; padding-bottom:0.372em;">mod</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top:0.372em; padding-bottom:0.372em;">10007</span></span></span></span></span> 的值。</p>
</div></div>

输入

<div class="ui bottom attached segment font-content"><div style="position: relative; overflow: hidden; "><p>第一行一个整数 <span class="katex"><span class="katex-mathml">tt</span><span class="katex-html"><span class="strut" style="height:0.61508em;"></span><span class="strut bottom" style="height:0.61508em; vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">t</span></span></span></span>，表示有 <span class="katex"><span class="katex-mathml">tt</span><span class="katex-html"><span class="strut" style="height:0.61508em;"></span><span class="strut bottom" style="height:0.61508em; vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">t</span></span></span></span> 组数据；</p>
<p>接下来 <span class="katex"><span class="katex-mathml">tt</span><span class="katex-html"><span class="strut" style="height:0.61508em;"></span><span class="strut bottom" style="height:0.61508em; vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">t</span></span></span></span> 行每行两个整数 <span class="katex"><span class="katex-mathml">n,mn, m</span><span class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em; vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span><span class="mpunct">,</span><span class="mord mathit">m</span></span></span></span>，如题意。</p>
</div></div>

输出

<div class="ui bottom attached segment font-content"><div style="position: relative; overflow: hidden; "><p><span class="katex"><span class="katex-mathml">tt</span><span class="katex-html"><span class="strut" style="height:0.61508em;"></span><span class="strut bottom" style="height:0.61508em; vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">t</span></span></span></span> 行，每行一个数，为 <span class="mjx-chtml"><span class="mjx-math"><span class="mjx-mrow"><span class="mjx-mrow"><span class="mjx-TeXmathchoice"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top:0.593em; padding-bottom:0.593em;">(</span></span></span></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width:0.621em;"><span class="mjx-numerator" style="font-size:70.7%; width:0.878em; top:-1.095em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top:0.225em; padding-bottom:0.298em;">n</span></span></span><span class="mjx-denominator" style="font-size:70.7%; width:0.878em; bottom:-0.524em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top:0.225em; padding-bottom:0.298em;">m</span></span></span></span><span style="height:1.144em; vertical-align:-0.37em;" class="mjx-vsize"></span></span><span class="mjx-TeXmathchoice"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top:0.593em; padding-bottom:0.593em;">)</span></span></span></span></span></span><span class="mjx-mo" style="padding-left:0.278em; padding-right:0.278em;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top:0.372em; padding-bottom:0.372em;">mod</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top:0.372em; padding-bottom:0.372em;">10007</span></span></span></span></span> 的答案。</p>
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提示

<div class="ui bottom attached segment font-content"><div style="position: relative; overflow: hidden; "><h4>样例输入</h4>
<div class="ui existing segment"><pre style="margin-top: 0; margin-bottom: 0; "><code class="lang-plain">4
5 1
5 2
7 3
4 2</code></pre></div>
<h4>样例输出</h4>
<div class="ui existing segment"><pre style="margin-top: 0; margin-bottom: 0; "><code class="lang-plain">5
10
35
6</code></pre></div>
</div></div>

<div class="ui bottom attached segment font-content"><div style="position: relative; overflow: hidden; "><p>对于全部数据，<span class="katex"><span class="katex-mathml">1≤t≤200,1≤m≤n≤2×1081le tle 200,1le mle nle 2	imes 10^8</span><span class="katex-html"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:1.008548em; vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span><span class="mrel">≤</span><span class="mord mathit">t</span><span class="mrel">≤</span><span class="mord mathrm">2</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mpunct">,</span><span class="mord mathrm">1</span><span class="mrel">≤</span><span class="mord mathit">m</span><span class="mrel">≤</span><span class="mord mathit">n</span><span class="mrel">≤</span><span class="mord mathrm">2</span><span class="mbin">×</span><span class="mord mathrm">1</span><span class="mord"><span class="mord mathrm">0</span><span class="vlist"><span style="top:-0.363em; margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathrm">8</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span></span></span></span>。</p>
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标签

一本通提高篇 10234 组合计数 Lucas 定理

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